Cantilever
A beam clamped at one end and loaded at free end is called a cantilever. Depression at the free end of a cantilever is given by δ = wl 3 / 3YIG
where, w = load, 1 = length of the cantilever,
y = Young’ s modulus of elasticity, and IG = geometrical moment of inertia. For a beam of rectangular cross-section having breadth b and thickness d. IG = bd 3 / 12 For a beam of circular cross-section area having radius r,
IG = π r 4 / 4
Beam Supported at Two Ends and Loaded at the Middle
Depression at middle δ = wl 3 / 48YIG Torsion of a Cylinder